20 papers · ranked by Valyu relevance
Evert Klaseboer, Qiang Sun
The famous scientist Hermann von Helmholtz was born 200 years ago. Many complex physical wave phenomena in engineering can effectively be described using one or a set of equations named after him: the Helmholtz equation. Although this has been known for a long time from a theoretical point of view, the actual numerical…
Antonio Stanziola, Simon R. Arridge, Bradley E. Treeby, Benjamin T. Cox
Efficient numerical solution of the acoustic Helmholtz equation in heterogeneous media remains challenging, particularly for large-scale problems with spatially-varying density—a limitation that restricts applications in biomedical acoustics and seismic imaging. We present a fast iterative solver that extends the…
Qiang Sun, Evert Klaseboer, Boo-Cheong Khoo, Derek Y. C. Chan
A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave…
Muhammad Nadeem, Zitian Li, Devendra Kumar, Yahya Alsayaad
The Helmholtz equation plays a crucial role in the study of wave propagation, underwater acoustics, and the behavior of waves in the ocean environment. The Helmholtz equation is also used to describe propagation through ocean waves, such as sound waves or electromagnetic waves. This paper presents the Elzaki transform…
Eelis Solala, Wen-Hua Xu, Pauli Parkkinen, Dage Sundholm
of Electric Response Properties Using the Bubbles and Cube Framework Authors: ['Eelis Solala' 'Wen-Hua Xu' 'Pauli Parkkinen' 'Dage Sundholm'] We have developed a fully numerical method for calculating the response of the Hartree-Fock orbitals to an external electric field. The Hartree-Fock orbitals are optimized using…
Younghoon Shin, Hojeong Kwak, Songky Moon, Sang-Bum Lee + 2 more
'Kyungwon An'] We report observation of an exceptional point in circular shell ultrasonic cavities in both theory and experiment. In our theoretical analysis we first observe two interacting mode groups, fluid- and solid-based modes, in the acoustic cavities and then show the existence of an EP of these mode groups…
Sameen Ahmed Khan, R. Jagannathan
An eight dimensional matrix representation of the Maxwell equations for a linear inhomogeneous medium has been derived earlier based on the Riemann-Silberstein-Weber vector starting from the equations satisfied by it. A new eight dimensional matrix representation, related to the earlier one by a similarity…
Nikolaos M. Papadakis, Georgios E. Stavroulakis, Giancarlo C. Righini
One of the uses of Helmholtz resonators is as sound absorbers for room acoustic applications, especially for the low frequency range. Their efficiency is centered around their resonance frequency which mainly depends on elements of their geometry such as the resonator volume and neck dimensions. Incorporating…
Damien F. G. Minenna, Khalil Aliane, Yves Elskens, A. Poyé + 3 more
'Frederic André' 'J. Puech' 'F. Doveil'] We propose a multi-particle self-consistent Hamiltonian (derived from an N-body description) that is applicable for periodic structures such as traveling-wave tubes (TWTs), gyrotrons, free-electron lasers, or particle accelerators. We build a 1D symplectic multi-particle…
Christopher Leon, Alexander Scheinker
We utilize a Fourier transformation-based representation of Maxwell’s equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier-Helmholtz-Maxwell neural operator method. In this approach, both of Gauss’s laws and Faraday’s law are built in as hard…
Guillermo Nuñez Ponasso, Derek A. Drumm, Hannes Oppermann, Abbie Wang + 5 more
Modern automated human head segmentations can generate high-resolution computational meshes involving many non-nested tissues. However, most source reconstruction software is limited to 3 –4 nested layers of low resolution and a small number of dipolar sources∼ 10, 000. Recently, we introduced modeling techniques for…
Nikolay Kuznetsov
Mean value properties of solutions to the m-dimensional Helmholtz and modified Helmholtz equations are considered. An elementary derivation of these properties is given; it involves the Euler–Poisson–Darboux equation. Despite the similar form of these properties for both equations, their consequences distinguish…
Mohsen Farshad
Providing a simple description of entropy as the foundation of thermodynamics is necessary for researchers in explaining physical phenomena in the universe. Here we dive deep into the meaning of entropy starting from the basics and ending with the Newton's second law of motion which may be rooted in a hidden dimension…
Michael J. A. Smith, I. David Abrahams
We present a solution method which combines the technique of matched asymptotic expansions with the method of multipole expansions to determine the band structure of cylindrical Helmholtz resonator arrays in two dimensions. The resonator geometry is considered in the limit as the wall thickness becomes very large…
Authors not listed
NMR chemical shifts depend on the applied magnetic flux density, and this becomes more and more important as stronger and stronger magnetic fields are becoming available. Herein, we develop a theory of the field dependence of NMR shifts of paramagnetic molecules in solution. Our derivation leads to two distinct…
Brian Pollack, Ryan Pellico, Cole Kampa, H.D. Glass + 1 more
'Michael Henry Schmitt'] The series solution to Laplace's equation in a helical coordinate system is derived and refined using symmetry and chirality arguments. These functions and their more commonplace counterparts are used to model solenoidal magnetic fields via linear, multidimensional curve-fitting. A judicious…
Ivan Fernandez‐Corbaton
The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Ivan Gligonov, Jörg Enderlein
Zernike polynomials are a sequence of orthogonal polynomials that play a crucial role in optics and in particular in modeling microscopy systems. Introduced by Frits Zernike in 1934, they are particularly useful in expressing wavefront aberrations and thus imperfections of imaging systems. However, their origin and…
Nick Gorkavyi
Bimolecular cell membranes play a crucial role in many biological processes and possess a unique set of physical properties. Bimolecular membranes and monomolecular films can be considered as a “two-dimensional fluid” because the diffusion of molecules along the membrane or film is a hydrodynamic process. On the other…